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arXiv · 1405.7770

Integral representations combining ladders and crossed-ladders

F. Bastianelli·A. Huet·C. Schubert·R. Thakur·A. Weber
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Abstract

We use the worldline formalism to derive integral representations for three classes of amplitudes in scalar field theory: (i) the scalar propagator exchanging N momenta with a scalar background field (ii) the "half-ladder" with N rungs in x - space (iii) the four-point ladder with N rungs in x - space as well as in (off-shell) momentum space. In each case we give a compact expression combining the N! Feynman diagrams contributing to the amplitude. As our main application, we reconsider the well-known case of two massive scalars interacting through the exchange of a massless scalar. Applying asymptotic estimates and a saddle-point approximation to the N-rung ladder plus crossed ladder diagrams, we derive a semi-analytic approximation formula for the lowest bound state mass in this model.

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F. Bastianelli, A. Huet, C. Schubert, R. Thakur, A. Weber. 2014-05-30. Integral representations combining ladders and crossed-ladders. https://doi.org/10.1007/jhep07(2014)066

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